There are four vampires in the southeastern Transylvanian Nosferatu clan. Zagor is the youngest, Arata is 200 years older than Zagor, Bela is 200 years older than Arata, and Horvath is 200 years older than Bela. The sum of all four ages is equal to 13,200. How old is Horvath?



This question is a basic consecutive numbers problem in which the solver is asked to find a series of consecutive numbers which, all together, sum to some number. For example, to find three consecutive numbers that total to 33, you simply set the smallest number at x, the next number will then be x+1, and the third number will be x+2. Altogether:



The same procedure can be followed to figure out the ages of the vampires in the southeastern Transylvanian Nosferatu clan. Set Zagor, the youngest, at Z. Then Arata is Z+200, Bela is Z+400, and Horvath is Z+600. All together, their ages total to 13,200. Therefore:



Other ways that this problem could also be solved include a little deductive thought. (First, allow me to divide each of the numbers by 100 so that we can dispense with all these zeroes and work in easier-to-handle figures. In this case, Zagor is 2 years older than Arata, Arata is 2 years older than Bela, and Horvath is 2 years older than Bela. Altogether, the sum of their ages is 132).

1. If the difference between the oldest (Horvath) and the youngest is 12 years, the number of years that they all have in common is 132-12 = 120. So, Zagor (the youngest) must be 120/4 = 30 x 100 = 3,000 years old, Arata is 3,200, Bela is 3,400, and Horvath is 3,600.

2. If the average age of the boys is 132/4 = 33 and the range of their ages is 0+2+2+2 = 6 years, then Zagor must be 3 years younger than the average, or 33-3 = 30 x 100 = 3,000, and Horvath must be 3 years older than the average, or 33+3 = 36 x 100 = 3,600 years old.

3. Similarly, if the average age of the boys is 33, then their ages must be somewhere around the 33 mark. Make a guess, keeping in mind that each must be two years older than the preceding:



And, once again, Horvath is the oldest, so he is 36 x 100 = 3,600 years old.

To check this answer, add up all the ages. Horvath is the eldest at 3,600 years of age. Bela is 200 years younger at 3,400. Arata is 200 years younger than Bela, or 3,200. Zagor is the baby at 3,000 years old. All together, 3,000 + 3,200 + 3,400 + 3,600 = 13,200 years.

And now we have an answer to a question which has plagued alt. vampyres for years... how old is Horvath, really?

Horvath is 3,600 years old.